MatricesHard
Question
Let M and N be two 3 × 3 non-singular skew symmetric matrices such that MN = NM. If PT denotes the transpose of P, then M2N2 (MTN)-1 (MN-1)T is equal to
Options
A.M2
B.-N2
C.-M2
D.MN
Solution
MN = NM
M2N2(MTN)-1(MN-1)T
M2N2N-1(MT)-1(N-1)T.MT
= M2N.(MT)-1(N-1)TMT = - M2.N(M)-1(NT)-1MT
= + M2NM-1N-1MT = - M.NMM-1N-1M = - MNN-1M = - M2.
Note: A skew symmetric matrix of order 3 cannot be non-singular hence the question is wrong.
M2N2(MTN)-1(MN-1)T
M2N2N-1(MT)-1(N-1)T.MT
= M2N.(MT)-1(N-1)TMT = - M2.N(M)-1(NT)-1MT
= + M2NM-1N-1MT = - M.NMM-1N-1M = - MNN-1M = - M2.
Note: A skew symmetric matrix of order 3 cannot be non-singular hence the question is wrong.
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